My Math Forum application of differentiation in economics

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 October 17th, 2012, 01:53 AM #1 Senior Member   Joined: Sep 2012 Posts: 112 Thanks: 0 application of differentiation in economics A monopolist produces x units of a commodity at a total cost of ax^2+bx+c and the demand law for the same is given by p= Q-Rx, where Q and R constants. A tax of Rs.K per unit is levied by the government. The manufacturer adds the tax to his cost. (a) find the price and the output both before and after tax. (b) show that the tax brings in maximum return when K=(Q-b)/2 I could solve the 1st question i.e. (a). But I don't know how to solve (b). Please help.
 October 17th, 2012, 10:39 AM #2 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: application of differentiation in economics Tax is maximized when the derivative of tax revenue is 0. First solve for tax revenue, then differentiate. Next set this equal to zero and solve. Finally, substitute back into the original.
October 17th, 2012, 11:00 PM   #3
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Re: application of differentiation in economics

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 Originally Posted by CRGreathouse Tax is maximized when the derivative of tax revenue is 0. First solve for tax revenue, then differentiate. Next set this equal to zero and solve. Finally, substitute back into the original.
Does that mean 'maximum return' refers to 'maximum total tax revenue' here???

 October 18th, 2012, 07:25 AM #4 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: application of differentiation in economics Yes.
October 28th, 2012, 09:37 AM   #5
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Re: application of differentiation in economics

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 Originally Posted by CRGreathouse Yes.
Thank you so much....

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